A MULTIBETA REPRESENTATION THEOREM FOR LINEAR ASSET PRICING THEORIES

This paper derives a multibeta representation theorem for pricing asse ts using arbitrary reference variables that are not necessarily the tr ue factors. Under this theorem, the upper bound on pricing deviations depends upon the correlations not only between the reference variables and the factors but also between the reference variables and the resi dual risks. A new concept of a well-diversified variable is introduced , which though free of residual risk, may be less than perfectly corre lated with the true factors. Well-diversified variables correlated wit h the factors play a key role in the pricing of assets, since these va riables can replace the factors without any loss in pricing accuracy u nder all linear asset pricing theories.